Formal Relationship between Petri Net and Graph Transformation Systems based on Functors between M-adhesive Categories

Various kinds of graph transformations and Petri net transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories, generalizing weak adhesive HLR categories. For typed attributed graph transformation systems, the tool environment AGG allows the modeling, the simulation and the analysis of graph transformations. A corresponding tool for Petri net transformation systems, the RON-Environment, has recently been developed which implements and simulates Petri net transformations based on corresponding graph transformations using AGG. Up to now, the correspondence between Petri net and graph transformations is handled on an informal level. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allow the translation of Petri net transformations into graph transformations with equivalent behavior, and, vice versa, the creation of Petri net transformations from graph transformations. Since this is supposed to work for different kinds of Petri nets, we propose to define suitable functors, called M-functors, between different M-adhesive categories and to investigate properties allowing us the translation and creation of transformations of the corresponding M-adhesive transformation systems

Functors between M-adhesive Categories Applied to Petri Net and Graph Transformation Systems

Various kinds of graph transformations and Petri net transformation systems are examples of M-adhesive transformation systems based on M-adhesive categories, generalizing weak adhesive HLR categories. For typed attributed graph transformation systems, the tool environment AGG allows the modeling, the simulation and the analysis of graph transformations. A corresponding tool for Petri net transformation systems, the RON-Environment, has recently been developed which implements and simulates Petri net transformations based on corresponding graph transformations using AGG. Up to now, the correspondence between Petri net and graph transformations is handled on an informal level. The purpose of this paper is to establish a formal relationship between the corresponding M-adhesive transformation systems, which allow the translation of Petri net transformations into graph transformations with equivalent behavior, and, vice versa, the creation of Petri net transformations from graph transformations. Since this is supposed to work for different kinds of Petri nets, we propose to define suitable functors, called M-functors, between different M-adhesive categories and to investigate properties allowing us the translation and creation of transformations of the corresponding M-adhesive transformation systems

Automating the transformation-based analysis of visual languages

The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)

The Conversion of Dynamic Fault Trees to Stochastic Petri Nets, as a case of Graph Transformation

AbstractA model-to-model transformation from Dynamic Fault Trees to Stochastic Petri Nets, by means of graph transformation rules, is presented in this paper. Dynamic Fault Trees (DFT) are used for the reliability analysis of complex and large systems and represent by means of gates, how combinations or sequences of component failure events, lead to the failure of the system. DFTs need the state space solution which can be obtained by converting a DFT to a Stochastic Petri Net: this task is expressed by means of graph transformation rules, and is applied to a case of system

Transfer of Local Confluence and Termination between Petri Net and Graph Transformation Systems Based on M-Functors: Extended Version

Recently, a formal relationship between Petri net and graph transformation systems has been established using the new framework of M-functors F : (C1;M1) -> (C2;M2) between M-adhesive categories. This new approach allows to translate transformations in (C1;M1) into corresponding transformations in (C2;M2) and, vice versa, to create transformations in (C1;M1) from those in (C2;M2). This is helpful because our tool for reconfigurable Petri nets, the RON-tool, performs the analysis of Petri net transformations by analyzing corresponding graph transformations using the AGG-tool. Up to now, this correspondence has been implemented as a converter on an informal level. The formal correspondence results given by our framework make the RON-tool more reliable. In this paper we extend this framework to the transfer of local confluence, termination and functional behavior. In particular, we are able to create these properties for transformations in (C1;M1) from corresponding properties of transformations in (C2;M2), where (C1;M1) are Petri nets with individual tokens and (C2;M2) typed attributed graphs. This allows us to apply the wellknown critical pair analysis for typed attributed graph transformations supported by the AGG-tool in order to analyze these properties for Petri net transformations

Operációkutatási módszerek műszaki informatikai rendszerek analízisében és verifikációjában = Operation Research Methods for the Analysis and Verification of Information Technology Systems

Kidolgoztuk a Petri-hálók és produkciós hálók (PNS) egységes szemléletű leírását. Megfogalmaztuk az "optimális trajektória generálásának" problémáját Petri-hálós modellekre. A megoldásként kidolgozott és implementált algoritmus egyúttal temporális logikai követelményeket is vizsgál a modellen. Az algoritmust gyorsítottuk a PNS logikai bázisa fölötti kereséssel. A SPIN modellellenőrzőt magát használva egy másik megoldást is adtunk a problémára, valamint gráftranszformációs rendszerek optimalizálására. Megadtuk a lineáris korlátozási feltételekkel adott szeparábilis konkáv minimalizálási feladat egy elégséges optimalitási kritériumát, mely a Branch-and-Bound típusú algoritmusban használható fel megállási kritériumként. A magasszintű leírásokból a Petri-hálós modellbe történő transzformációkat matematikai alapokon definiáltuk, megvalósításukra automatikus modelltranszformációs megoldást dolgoztunk ki: egy algoritmust, amely GRM profillal adott modellből generálja a Petri-hálót, és egy általános algoritmust, amely UML modellekből származtat a diagnosztika alapjául szolgáló modelleket. Megvizsgáltuk ezen modellek illeszthetőségét a szabványokhoz. Multiprocesszoros rendszerek diagnosztizálására egy PNS technikákat használó algoritmust adtunk, melynek várható hatékonyságát igazoltuk. Munkálatok folytak a diagnosztika tesztalapú megközelítésére, és diagnosztikai modellek kísérletes paraméterezésére. Kísérleteket végeztünk az IBM Holosofx ipari workflow modellező eszköz illesztésére. | A unified treatment for Petri nets and process network (PNS) problems was defined. The 'optimal trajectory generation problem' for Petri nets was defined. Elaboration and implementation of an algorithm that is able not only to give the optimal trajectory but to verify temporal logic requirements for Petri nets. This algorithm was accelerated using Branch-and-Bound method over the logical basis of the feasible process networks. Another algorithm to solve the problem using only the SPIN model checker was elaborated. The optimization of graph transformation systems with time was solved based on the same technique. A sufficient optimality criteria was given for constrained, concave minimization problems. The precise mathematics of the model transformation from high-level models to Petri nets was defined, and automatic model transformations were carried out to realize these transformations: a transformation from UML models given by the GRM profile to Petri nets and a general algorithm that delivers models to diagnose from UML models. The conformancy of these models to standards was investigated. The probabilistic diagnosis problem in multiprocessor systems was solved using PNS techniques. The efficiency of the method was shown. There were efforts to elaborate a test-based approach of diagnostics, and to parameterize diagnostics models based on dependability experiments. Experiments were carried out to transform IBM Holosofx models to Petri nets

Transfer of Local Confluence and Termination between Petri Net and Graph Transformation Systems Based on M-Functors

Recently, a formal relationship between Petri net and graph transformation systems has been established using the new framework of M-functors F : (C1;M1) -> (C2;M2) between M-adhesive categories. This new approach allows to translate transformations in (C1;M1) into corresponding transformations in (C2;M2) and, vice versa, to create transformations in (C1;M1) from those in (C2;M2). This is helpful because our tool for reconfigurable Petri nets, the RONtool, performs the analysis of Petri net transformations by analyzing corresponding graph transformations using the AGG-tool. Up to now, this  correspondence has been implemented as a converter on an informal level. The formal correspondence results given by our framework make the RON-tool more reliable.In this paper, we extend this framework to the transfer of local confluence, termination and functional behavior. In particular, we are able to create these properties for transformations in (C1;M1) from corresponding properties of transformations in (C2;M2), where (C1;M1) are Petri nets with individual tokens and (C2;M2) typed attributed graphs. This allows us to apply the well-known critical pair analysis for typed attributed graph transformations supported by the AGG-tool in order to analyze these properties for Petri net transformations

Basic Results for Two Types of High-Level Replacement Systems1 1Research partially supported by the European Community under TMR Network GETGRATS and the ESPRIT Working Group APPLIGRAPH.

AbstractThe general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class M . Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism K → L belongs to M

Translating model simulators to analysis models

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-78743-3_6Proceedings of 11th International Conference, FASE 2008, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2008, Budapest, Hungary, March 29-April 6, 2008.We present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language by means of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets.Work sponsored by the Spanish Ministry of Science and Education, project MOSAIC (TSI2005-08225-C07-06

Refactoring of Model Transformations

Model-to-model transformations between visual languages are often defined by typed, attributed graph transformation systems. Here, the source and target languages of the model transformation are given by type graphs (or meta models), and the relation between source and target model elements is captured by graph transformation rules. On the other hand, refactoring is a technique to improve the structure of a model in order to make it easier to comprehend, more maintainable and amenable to change. Refactoring can be defined by graph transformation rules, too. In the context of model transformation, problems arise when models of the source language of a model transformation become subject to refactoring. It may well be the case that after the refactoring, the model transformation rules are no longer applicable because the refactoring induced structural changes in the models. In this paper, we consider a graph-transformation-based evolution of model transformations which adapts the model transformation rules to the refactored models. In the main result, we show that under suitable assumptions, the evolution leads to an adapted model transformation which is compatible with refactoring of the source and target models. In a small case study, we apply our techniques to a well-known model transformation from statecharts to Petri nets